Good day.
Please look at MCU Client example (source on GitHub). This can mix participant streams into one room stream which can be republished to RTMP server using REST API
The Screen Sharing example (source on GitHub) shows how to publish screen sharing stream. You can add the stream to MCU mixer by name, for example, desktop#room1. In this case, screen share stream will be displayed like this
Please read also this article about MCU conference implementation and this article about screen sharing